A failed asylum seeker was due to be deported to Nigeria despite an ongoing police investigation into allegations that she was raped in Britain.

Women's groups and her MP have called for the Home Office to defer her deportation until the investigation is concluded.

The woman, 41, has been told by Thames Valley police that the man she claims raped her has been arrested but was granted bail, pending further inquiries. In a letter to her, seen by the Guardian, dated 6 June, police have told her that the investigation is continuing and that she should stay in touch via email if she is deported.

Speaking from Yarl's Wood detention centre, where she is being kept on suicide watch, the woman said: "They said if I go to Nigeria I should send an email about the facts. But if I go back to Nigeria I don't have access to a computer. I don't even know how to use a computer."

Her MP, Andrew Smith, said he had written several letters to Damian Green, the minister for immigration, and the UK Border Agency about the "compassionate and compelling circumstances" of the woman's case, but had received no written replies. The Labour MP for Oxford East said: "There are sufficient questions in this woman's case that her deportation should at the very least be deferred. She ought to have the opportunity to make a proper legal case and the alleged rape should be investigated and the perpetrator brought to justice."

Kiki Axelsson, a spokeswoman for Women Against Rape, which is helping her with her case, said: "This woman was raped in the UK. She must not be deported before this serious crime is investigated, but the Home Office is refusing to stop her deportation. If deported, she would be unable to be a witness in any ongoing investigation or trial. In addition they are deporting a rape survivor to a situation where she is further at risk."

The woman, who says she is a victim of forced marriage and was threatened with female genital mutilation by her husband's family before being trafficked into Britain, claimed asylum in March this year but was refused in April by the Border Agency after her evidence was found to be contradictory.

Her account of the rape, which happened in February this year but which she did not report until she was taken to Yarl's Wood, was also questioned as a result.

When asked about why she did not report the rape to the police earlier, she said she was afraid of the police and did not want her boyfriend to know because he would consider her "a dirty person" as a result. She said she was given welfare advice at the detention centre and felt able to report the rape.

A spokeswoman for Thames Valley police said: "We can confirm that a rape has been reported to us and that [a] 41-year-old man was has arrested and releases on bail till 11 July."

A UK Border Agency spokesperson said: "The police have confirmed they have no objections to this individual being removed and that it will not compromise their investigation.

"All aspects of this individual's immigration case were considered fully and dismissed by the courts. There is no legal basis for her to remain in the UK and therefore removal is appropriate."